Studies in vortex motion
暂无分享,去创建一个
This thesis covers four different problems in the
understanding of vortex sheets, and these are presented in
four chapters. In Chapter 1, free streamline theory is used to determine
the steady solutions of an array of identical, hollow
or stagnant core vortices in an inviscid, incompressible
fluid. Assuming the array is symmetric to rotation through
π radians about an axis through any vortex centre, there
are two solutions or no solutions depending on whether A^(1/2)/L
is less than or greater than 0.38 where A is the area of
the vortex and L is the separation distance. Stability
analysis shows that the more deformed shape is unstable to
infinitesimal symmetric disturbances which leave the centres
of the vortices undisplaced. Chapter 2 is concerned with the roll-up of vortex
sheets in homogeneous fluid. The flow over conventional and
ring wings is used to test the method of Fink and Soh (1974).
Despite modifications which improve the accuracy of the
method, unphysical results occur. A possible explanation
for this is that small scales are important and an alternate
method based on "Cloud-in-Cell" techniques is introduced.
The results show small scale growth and amalgamation into
larger structures. The motion of a buoyant pair of line vortices of
opposite circulation is considered in Chapter 3. The density
difference between the fluid carried by the vortices and the
fluid outside is considered small, so that the Boussinesq
approximation may be used. A macroscopic model is developed
which shows the formation of a detrainment filament and this
is included as a modification to the model. The results
agree well with the numerical solution as developed by Hill
(1975b) and show that after an initial slowdown, the vortices
begin to accelerate downwards. Chapter 4 reproduces completely a paper that has
already been published (Baker, Barker, Bofah and Saffman
(1974)) on the effect of "vortex wandering" on the measurement
of velocity profiles of the trailing vortices behind a
wing.